At Trinity College a new world opened out before the country-bred lad. He knew his classics passably, but of mathematics and science he was ignorant, except through the smatterings he had picked up for himself. He devoured a book on logic, and another on Kepler's Optics, so fast that his attendance at lectures on these subjects became unnecessary. He also got hold of a Euclid and of Descartes's Geometry. The Euclid seemed childishly easy, and was thrown aside, but the Descartes baffled him for a time. However, he set to it again and again and before long mastered it. He threw himself heart and soul into mathematics, and very soon made some remarkable discoveries. First he discovered the binomial theorem: familiar now to all who have done any algebra, unintelligible to others, and therefore I say nothing about it. By the age of twenty-one or two he had begun his great mathematical discovery of infinite series and fluxions--now known by the name of the Differential Calculus. He wrote these things out and must have been quite absorbed in them, but it never seems to have occurred to him to publish them or tell any one about them. In 1664 he noticed some halos round the moon, and, as his manner was, he measured their angles--the small ones 3 and 5 degrees each, the larger one 22°·35. Later he gave their theory. Small coloured halos round the moon are often seen, and are said to be a sign of rain. They are produced by the action of minute globules of water or cloud particles upon light, and are brightest when the particles are nearly equal in size. They are not like the rainbow, every part of which is due to light that has entered a raindrop, and been refracted and reflected with prismatic separation of colours; a halo is caused by particles so small as to be almost comparable with the size of waves of light, in a way which is explained in optics under the head "diffraction." It may be easily imitated by dusting an ordinary piece of window-glass over with lycopodium, placing a candle near it, and then looking at the candle-flame through the dusty glass from a fair distance. Or you may look at the image of a candle in a dusted looking-glass. Lycopodium dust is specially suitable, for its granules are remarkably equal in size. The large halo, more rarely seen, of angular radius 22°·35, is due to another cause again, and is a prismatic effect, although it exhibits hardly any colour. The angle 22-1/2° is characteristic of refraction in crystals with angles of 60° and refractive index about the same as water; in other words this halo is caused by ice crystals in the higher regions of the atmosphere.